Database Reference
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more confusing. In the final analysis, it is the transparency, the business meaning,
and the usability that count. Analysts should be able to clearly recognize what each
factor represents in order to use it in upcoming tasks.
WHAT IS THE MEANING OF EACH COMPONENT?
The next task is to determine the meaning of the derived components, with respect
to the original fields. The goal is to understand the information that they convey and
name them accordingly. This interpretation is based on the correlations among the
derived components and the original inputs by examination of the corresponding
loadings.
Rotation is a recommended technique to apply in order to facilitate the
interpretation process of the components. Rotation minimizes the number of fields
that are strongly correlated with many components and attempts to associate each
input to one component. There are numerous rotation techniques, with Varimax
being the most popular for data reduction purposes since it yields transparent
components which are also uncorrelated, a characteristic usually required for
subsequent tasks. Thus, instead of looking at the component matrix and its loadings,
we will examine the rotated component matrix which results after application of a
Varimax rotation.
Technical Tips on Rotation Methods
Rotation is a method used to simplify the interpretation of components. It
attempts to clarify situations in which fields seem to be associated with more
than one component. It tries to produce a solution in which each component
has large (
1) correlations with a specific set of original inputs and
negligible correlations (close to 0) with the rest of the fields.
As mentioned above, components are extracted in order of significance,
with the first one accounting for as much of the input variance as possible
and subsequent components accounting for residual variance. Subsequently,
the first component is usually a general component with most of the inputs
associated to it. Rotation tries to fix this and redistributes the explained
variance in order to produce a more efficient and meaningful solution. It does
so by rotating the reference axes of the components, as shown in Figure 3.2,
so that the correlation of each component with the original fields is either
minimized or maximized.
Varimax rotation moves the axes so that the angle between them remains
perpendicular, resulting in uncorrelated components (orthogonal rotation).
+
1,
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